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Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
You may return the answer in any order.
Input: n = 4, k = 2
[ [2,4], [3,4], [2,3], [1,2], [1,3], [1,4], ]
Input: n = 1, k = 1
- NOTE: I highly recommend going through the Backtracking chapters in the order they are given in the Index page to get the most out of it and be able to build a rock-solid understanding.
Writing algorithm for this problem is easy if you already know how to compute combinations manually using pen and paper. If you know how to find combinations manually, you just reverse-engineer the process to devise the algorithm.
If we are trying to find all possible combinations of size k out of n numbers from 1 to n, then the first position of the combination can have all n numbers, for each of these n numbers in the first position the second position can have (n - 1) numbers because we cannot include the number in a combination for second position which is already present in the first position. Proceeding in this way k-th position of the combination can have only (n - k + 1) numbers.
Speaking in the terms of Backtracking, the candidates for the 1st position of combination are all n numbers from 1 to n, 2nd position can have (n - 1) numbers which does not include the number present in the 1st position of the combination. Moving forward in this way, candidates for the kth position of a combination would be (n - k + 1) numbers not present in any of the previous (k - 1) positions in the current combination.
We will implement the above described algorithm using our Backtracking Template as follows:
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Don't forget to take in-depth look at the other backtracking problems because that is what would make you comfortable with using the backtracking template and master the art of Backtracking:
- Letter Case Permutation
- Power Set
- All Paths Between Two Nodes
- Word Search
- Word Square
- Generate Parentheses
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